PSI - Issue 48

Nikola Raičević et al. / Procedia Structural Integrity 48 (2023) 342 – 347 Raičević et al / Structural Integrity Procedia 00 (2023) 000 – 000

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The finite element method, implemented in commercial ANSYS software was applied. Since HPT case is exposed to pressure and heat, special attention was paid to the applied load which involved thermal conditions. The approach involved evaluation of stress intensity factors (SIFs), paths of crack growth predictions and a fatigue life evaluation through an incremental crack extension analysis. The linear-elastic fracture mechanics assumptions were used. Separating Morphing and Adaptive Remeshing Technology (S.M.A.R.T.), which relies on the Unstructured Mesh Method (UMM) implemented in ANSYS has been used for the crack paths predictions ( Đukić et al. (2020 ), Kastratović et al. (2020) ). This numerical analysis was conducted in order to simulate crack propagation which had to match the one observed in the workshop (Fig. 5.). The Paris law model has been employed for the evaluation of the fatigue life which corresponds to the observed crack’s length.

Fig. 5. Crack propagation.

To obtain required Paris coefficients a multi-objective genetic algorithm (MOGA), implemented through response surface optimization (RSO) – another module of ANSYS – was used. MOGA, as a global optimizer is more suitable for global optima searching, especially in the case of the multi-objective optimization, as it can be seen in Deb et al. (2002), Deb and Tiwari (2008), Shukla and Deb (2007). The sorting mechanism of the sample set (decision support process) represents weighted, aggregation-based and goal-based design ranking technique. Within the RSO, design of experiments (DOE) is applied to generate numerical experimental points. These points are used to build meta-model functions in which the output parameters are described in terms of the input parameters. The standard response surface type - full second order polynomials was used for meta-modelling. The objectives of this optimization i.e., output parameters, were the crack length and the corresponding number of cycles of crack growth, while input parameters, i.e., design variables, were Paris coefficients, C and m. For the purpose of establishing the suitable exploring domain, lower and upper boundaries of input parameters were being investigated. Several different domains were investigated until adequate range was established. The range of the design variables is presented in Table 1.

Table 1. Lower and upper boundaries of input parameters. Design variables Initial values

Lower and upper boundaries

Constant C Constant m

1e-13

5e-14 – 5e-13

3.75

3

–

4.5

Based on the conducted computations, for required conditions, Paris coefficients of applied material are obtained as C= 1.5396e -13 , and m= 3.305. These results had to be verified by the FEM analysis. The verification showed that determined Paris coefficients indeed gave number of cycles which corresponds to the observed crack’s length (Fig. 6.).